Question

You invest $100 in a risky asset with an expected rate of return of 0.11 and a standard deviation of 0.21, along with a T-bill with a rate of return of 0.045. A portfolio that has an expected outcome and risk profile different from either the risky asset or the T-bill can be constructed by allocating your investment between the two assets. The combination of the risky asset and the risk-free T-bill will result in a portfolio with a unique expected return and risk level, which can be determined based on the allocation or weight given to each asset in the portfolio. This allocation decision will depend on your risk tolerance and return objectives.

Answer 1

The student's question deals with combining a risky asset and a risk-free T-bill to create a diversified investment portfolio that balances risk and expected return based on individual preferences. Investment options like bank accounts, bonds, and stocks demonstrate the risk-return tradeoff where higher risk is typically associated with higher potential returns. Portfolio expected return can be tailored through diversification and allocation decisions.

Step-by-step explanation:

The question explores the concept of portfolio diversification in finance, where an investor allocates their money between different assets with varying risk and expected return profiles to achieve a balance that suits their risk tolerance and investment goals. Specifically, it mentions combining a risky asset with a known expected return and standard deviation with a risk-free T-bill with a lower return. This strategy can create a portfolio with a unique expected return and risk level, distinct from holding either the risky asset or the T-bill alone.

Household investment choices, such as bank accounts, bonds, and stocks, illustrate the tradeoff between expected return and risk. Bank accounts offer low risk and low returns, while stocks provide higher potential returns but with increased risk. Bonds sit in between, offering higher returns than bank accounts but with less risk compared to stocks. Over time, stocks have shown higher average returns compared to bonds due to their higher risk level. A high-risk investment does not necessarily mean a low return; rather, it indicates a wider range of possible outcomes. High-risk investments generally demand higher expected returns to compensate investors for taking on more risk.

The combination of investments in a portfolio determines the overall expected rate of return and the risk level. Individual assets can vary significantly in their returns, but diversification can help balance these fluctuations, potentially leading to more consistent overall portfolio performance. To calculate the expected portfolio return, one can use the formula: Principal + (principal × rate x time).